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Kevin Lin
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If the spectral radius of matrix $A$ is less than $1$, how to construct a positive definite $Q$ such that $Q - A^{H}QA$ is also positive definite?
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If the spectral radius of matrix $A$ is less than $1$, how to construct a positive definite $Q$ such that $Q - A^{H}QA$ is also positive definite?
@GiorgioMetafune (I am afraid my English expression could be inappropriate or unclear at times.) You can try to take a norm such that ||A|| is less than 1. Matrix Analysis by Roger and Charles may be helpful. You can find information about the connection between spectral radius and matrix norm, as well as the convergence of matrix series in that book.
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If the spectral radius of matrix $A$ is less than $1$, how to construct a positive definite $Q$ such that $Q - A^{H}QA$ is also positive definite?
@Jochen Glueck Thank you very much. Now I can understand the "magic" construction of Q. And I really appreciate your helping me edit my question.
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 Student
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If the spectral radius of matrix $A$ is less than $1$, how to construct a positive definite $Q$ such that $Q - A^{H}QA$ is also positive definite?